MIXED INTEGER-DISCRETE-CONTINUOUS OPTIMIZATION BY DIFFERENTIAL EVOLUTION Part 1: the optimization method

This article discusses solving non-linear programming problems containing integer, discrete and continuous variables. The Part 1 of the article describes a novel optimization method based on Differential Evolution algorithm. The required handling techniques for integer, discrete and continuous variables are described including the techniques needed to handle boundary constraints as well as those needed to simultaneously deal with several non-linear and non-trivial constraint functions. In Part 2 of the article a mechanical engineering design related numerical example, design of a coil spring, is given to illustrate the capabilities and the practical use of the method. It is demonstrated that the described approach is capable of obtaining high quality solutions. The novel method is relatively easy to implement and use, effective, efficient and robust, which makes it as an attractive and widely applicable approach for solving practical engineering design problems.